1: I search it on my primary search engine (Google), generally the first lines of results.
2: I change the search string, apply filters and search it again.
3: I search it on sites I love, assuming that someone would have covered it, like MakeUseOf, stackoverflow, quora.com etc.
4: I use other search engines like blekko.com or Bing.
5: Find some site or forum related to topic and ask it there.

Now I want steps 1, 3, and 4 to be automated by some browser extension by using multiple tabs since websites are fixed.

Other then that Google already does everything you want using search parameters.
If you want to search the entire internet: put in your search string "hello world".
If you want so search on a specific site you can easily do that by limiting the results "hello world site:makeuseof.com" or "hello world site:stackoverflow.com".